S数
题目大意：
定义f(x)为x各位数字之和，问[l,r]区间内有多少数满足f(x)*f(x)=f(x*x)。
思路：
刚开始暴力打表，发现所有数的位都在0..3之间，然后直接枚举每一位，最坏情况下运算规模大概是9^4。
然后本来的表也不舍得扔掉，所以就一半打表一半标算。
然后发现打表+标算其实反而会比直接上标算慢。
1 #include<cstdio> 2 #include<cctype> 3 #include<algorithm> 4 inline int getint() { 5 register char ch; 6 while(!isdigit(ch=getchar())); 7 register int x=ch^'0'; 8 while(isdigit(ch=getchar())) x=(((x<<2)+x)<<1)+(ch^'0'); 9 return x; 10 } 11 const int table[]={-1,0,1,2,3,10,11,12,13,20,21,22,30,31,100,101,102,103,110,111,112,113,120,121,122,130,200,201,202,210,211,212,220,221,300,301,310,311,1000,1001,1002,1003,1010,1011,1012,1013,1020,1021,1022,1030,1031,1100,1101,1102,1103,1110,1111,1112,1113,1120,1121,1122,1130,1200,1201,1202,1210,1211,1212,1220,1300,1301,2000,2001,2002,2010,2011,2012,2020,2021,2022,2100,2101,2102,2110,2111,2120,2121,2200,2201,2202,2210,2211,3000,3001,3010,3011,3100,3101,3110,3111,10000,10001,10002,10003,10010,10011,10012,10013,10020,10021,10022,10030,10031,10100,10101,10102,10103,10110,10111,10112,10113,10120,10121,10122,10130,10200,10201,10202,10210,10211,10212,10220,10221,10300,10310,11000,11001,11002,11003,11010,11011,11012,11013,11020,11021,11022,11030,11031,11100,11101,11102,11103,11110,11111,11112,11113,11120,11121,11122,11130,11200,11201,11202,11210,11211,11220,11300,12000,12001,12002,12010,12011,12012,12020,12100,12101,12102,12110,12111,12120,12200,12201,12202,13000,13001,13010,13011,20000,20001,20002,20010,20011,20012,20020,20021,20022,20100,20101,20102,20110,20111,20112,20120,20121,20122,20200,20201,20210,20211,20220,20221,21000,21001,21002,21010,21011,21020,21021,21100,21101,21102,21110,21111,21200,21201,21210,22000,22001,22002,22010,22011,22020,22100,22101,22102,22110,22111,30000,30001,30010,30011,30100,30101,30110,30111,31000,31001,31010,31011,31100,31101,31110,31111,100000,100001,100002,100003,100010,100011,100012,100013,100020,100021,100022,100030,100031,100100,100101,100102,100103,100110,100111,100112,100113,100120,100121,100122,100130,100200,100201,100202,100210,100211,100212,100220,100221,100300,100301,100310,100311,101000,101001,101002,101003,101010,101011,101012,101013,101020,101021,101022,101030,101031,101100,101101,101102,101103,101110,101111,101112,101113,101120,101121,101122,101130,101200,101201,101202,101210,101211,101212,101220,101300,101301,102000,102001,102002,102010,102011,102012,102020,102021,102022,102100,102101,102102,102110,102111,102120,102121,102200,102210,103000,103001,103100,103101,110000,110001,110002,110003,110010,110011,110012,110013,110020,110021,110022,110030,110031,110100,110101,110102,110103,110110,110111,110112,110113,110120,110121,110122,110130,110200,110201,110202,110210,110211,110212,110220,110221,110300,110310,111000,111001,111002,111003,111010,111011,111012,111013,111020,111021,111022,111030,111031,111100,111101,111102,111103,111110,111111,111112,111120,111121,111130,111200,111201,111202,111210,111211,111220,111300,112000,112001,112002,112010,112011,112012,112020,112100,112101,112102,112110,112111,112200,113000,113001,120000,120001,120002,120010,120011,120012,120020,120100,120101,120102,120110,120111,120112,120120,120200,120201,121000,121001,121002,121010,121011,121020,121100,121101,121102,121110,121111,121200,121201,122000,122001,122002,122010,122011,122020,130000,130001,130010,130011,130100,130101,130110,130111,200000,200001,200002,200010,200011,200012,200020,200021,200022,200100,200101,200102,200110,200111,200112,200120,200121,200122,200200,200201,200202,200210,200211,200212,200220,200221,201000,201001,201002,201010,201011,201012,201020,201021,201022,201100,201101,201110,201111,201120,201121,201200,201201,201210,201211,201220,202000,202001,202002,202010,202011,202012,202100,202101,202110,202111,202200,202210,210000,210001,210002,210010,210011,210020,210021,210100,210101,210102,210110,210111,210200,210201,210202,210210,210211,211000,211001,211002,211010,211011,211020,211021,211100,211101,211110,211111,212000,212001,212002,212010,212011,212100,212101,220000,220001,220002,220010,220011,220020,220100,220101,220102,220110,220111,220200,220201,221000,221001,221002,221010,221011,221020,221100,221101,221110,300000,300001,300010,300011,300100,300101,300110,300111,301000,301001,301010,301011,301100,301101,301110,301111,310000,310001,310010,310011,310100,310101,310110,310111,311000,311001,311010,311011,311100,311101,311110,1000000,1000001,1000002,1000003,1000010,1000011,1000012,1000013,1000020,1000021,1000022,1000030,1000031,1000100,1000101,1000102,1000103,1000110,1000111,1000112,1000113,1000120,1000121,1000122,1000130,1000200,1000201,1000202,1000210,1000211,1000212,1000220,1000221,1000300,1000301,1000310,1000311,1001000,1001001,1001002,1001003,1001010,1001011,1001012,1001013,1001020,1001021,1001022,1001030,1001031,1001100,1001101,1001102,1001103,1001110,1001111,1001112,1001113,1001120,1001121,1001122,1001130,1001200,1001201,1001202,1001210,1001211,1001212,1001220,1001300,1001301,1002000,1002001,1002002,1002010,1002011,1002012,1002020,1002021,1002022,1002100,1002101,1002102,1002110,1002111,1002120,1002121,1002200,1002201,1002202,1002210,1002211,1003000,1003010,1003100,1003110,1010000,1010001,1010002,1010003,1010010,1010011,1010012,1010013,1010020,1010021,1010022,1010030,1010031,1010100,1010101,1010102,1010103,1010110,1010111,1010112,1010113,1010120,1010121,1010122,1010130,1010200,1010201,1010202,1010210,1010211,1010212,1010220,1010221,1010300,1010310,1011000,1011001,1011002,1011003,1011010,10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12 const int SIZE=sizeof table/sizeof(int); 13 long long calc(const long long &x) { 14 long long sum=0,tmp=x; 15 while(tmp) { 16 sum+=tmp%10; 17 tmp/=10; 18 } 19 return sum; 20 } 21 int dfs(const long long &now,const int &r) { 22 if(now>r) return 0; 23 int ret=0; 24 if(calc(now)*calc(now)==calc(now*now)) ret++; 25 for(long long i=0;i<=3;i++) { 26 ret+=dfs(now*10+i,r); 27 } 28 return ret; 29 } 30 int main() { 31 freopen("snum.in","r+",stdin); 32 freopen("snum.out","w+",stdout); 33 int l=getint(),r=getint(); 34 if(r<=1e8) { 35 printf("%d\n",std::upper_bound(&table[0],&table[SIZE],r)-std::lower_bound(&table[0],&table[SIZE],l)); 36 return 0; 37 } 38 int ans=0; 39 if(l<=1e8) { 40 ans=1; 41 ans+=dfs(1,r); 42 ans+=dfs(2,r); 43 ans+=dfs(3,r); 44 ans-=std::lower_bound(&table[0],&table[SIZE],l)-&table[1]; 45 } else { 46 ans+=dfs(1,r); 47 ans+=dfs(2,r); 48 ans+=dfs(3,r); 49 ans-=dfs(1,l-1); 50 ans-=dfs(2,l-1); 51 ans-=dfs(3,l-1); 52 } 53 printf("%d\n",ans); 54 fclose(stdin); 55 fclose(stdout); 56 return 0; 57 }
